A308822 Sum of all the parts in the partitions of n into 5 parts.

0, 0, 0, 0, 0, 5, 6, 14, 24, 45, 70, 110, 156, 234, 322, 450, 592, 799, 1026, 1330, 1680, 2121, 2618, 3243, 3936, 4800, 5746, 6885, 8148, 9657, 11310, 13237, 15360, 17820, 20502, 23590, 26928, 30747, 34884, 39546, 44600, 50266, 56364, 63167, 70488, 78615

Offset

0,6

Links

Table of n, a(n) for n=0..45.

Index entries for sequences related to partitions

Formula

a(n) = n * A026811(n).

a(n) = A308823(n) + A308824(n) + A308825(n) + A308826(n) + A308827(n).

Example

The partitions of n into 5 parts for n = 10, 11, ..
                                                       1+1+1+1+10
                                                        1+1+1+2+9
                                                        1+1+1+3+8
                                                        1+1+1+4+7
                                                        1+1+1+5+6
                                            1+1+1+1+9   1+1+2+2+8
                                            1+1+1+2+8   1+1+2+3+7
                                            1+1+1+3+7   1+1+2+4+6
                                            1+1+1+4+6   1+1+2+5+5
                                            1+1+1+5+5   1+1+3+3+6
                                1+1+1+1+8   1+1+2+2+7   1+1+3+4+5
                                1+1+1+2+7   1+1+2+3+6   1+1+4+4+4
                                1+1+1+3+6   1+1+2+4+5   1+2+2+2+7
                    1+1+1+1+7   1+1+1+4+5   1+1+3+3+5   1+2+2+3+6
                    1+1+1+2+6   1+1+2+2+6   1+1+3+4+4   1+2+2+4+5
                    1+1+1+3+5   1+1+2+3+5   1+2+2+2+6   1+2+3+3+5
        1+1+1+1+6   1+1+1+4+4   1+1+2+4+4   1+2+2+3+5   1+2+3+4+4
        1+1+1+2+5   1+1+2+2+5   1+1+3+3+4   1+2+2+4+4   1+3+3+3+4
        1+1+1+3+4   1+1+2+3+4   1+2+2+2+5   1+2+3+3+4   2+2+2+2+6
        1+1+2+2+4   1+1+3+3+3   1+2+2+3+4   1+3+3+3+3   2+2+2+3+5
        1+1+2+3+3   1+2+2+2+4   1+2+3+3+3   2+2+2+2+5   2+2+2+4+4
        1+2+2+2+3   1+2+2+3+3   2+2+2+2+4   2+2+2+3+4   2+2+3+3+4
        2+2+2+2+2   2+2+2+2+3   2+2+2+3+3   2+2+3+3+3   2+3+3+3+3
--------------------------------------------------------------------------
  n  |     10          11          12          13          14        ...
--------------------------------------------------------------------------
a(n) |     70         110         156         234         322        ...
--------------------------------------------------------------------------
- Wesley Ivan Hurt, Sep 08 2019

Mathematica

Table[n*Sum[Sum[Sum[Sum[1, {i, j, Floor[(n - j - k - l)/2]}], {j, k, Floor[(n - k - l)/3]}], {k, l, Floor[(n - l)/4]}], {l, Floor[n/5]}], {n, 0, 100}]

Crossrefs

Cf. A026811, A308823, A308824, A308825, A308826, A308827.

Sequence in context: A322479 A309480 A180686 * A289190 A145491 A282466

Adjacent sequences: A308819 A308820 A308821 * A308823 A308824 A308825

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 26 2019

Status

approved